ANOVA

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ANOVA

• Using Regression Analysis on Categories

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Three Independent Groups

• One Dependent Variable

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Experiment

• Improving Memory

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Population and Sample

• Population Patients Suffering from Korsakoff
  Psychosis
• Randomly Select Nine Patients

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Random Assignment
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Experimental Treatments
Group 1 Placebo Group 2 Dexfermetrazine
Group 3 Physostigmine
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Dependent Variable

• Number of Nonsense Syllabi Remembered

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Do the three groups differ onthe dependent
variable?
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Record Data
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Predict Y from X
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Scatterplot for X and Y
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Regression Analysison Categories

• Compute the group means

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Predicted Scores
The vector of predicted scores consists of group
means.
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Scatterplot for X and Y
There is a non-linear relationship.
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Error Scores Y - Y Y
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Variance Components
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Variance Components
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What percentage of variance in Y was accounted
for bythe group membership?
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Standard Variance Components

• Predicted Standard Variance
• Error Standard Variance

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Standard Variance Components
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Percentage Accounted For
X accounts for 17 of the variance in Y.
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Do the three groups differ onthe dependent
variable?
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Statistical Inference

• Methods for generalizing from samples to the
  populations

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Degrees of Freedom

• There are three groups. The degrees of freedom
  associated with the predicted component equals 3
  - 1 2
• There are nine subjects. The degrees of freedom
  associated with the error component equal 9 - 3
  6

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The F ratio
Predicted Standard Variance
Error Standard Variance
k is the number of groups n is the number of
subjects
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Compute the F ratio
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ANOVA TableStandard Variance Components
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The three groups do not differ onthe dependent
variable.The drugs do not improve the patients
memory.